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Typical dynamics of volume preserving homeomorphisms /
This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typic...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2000.
|
| Colección: | Cambridge tracts in mathematics ;
139. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Alpern, Steve, |d 1948- | |
| 245 | 1 | 0 | |a Typical dynamics of volume preserving homeomorphisms / |c Steve Alpern, V.S. Prasad. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2000. | ||
| 300 | |a 1 online resource (xix, 216 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a Cambridge tracts in mathematics ; |v 139 | |
| 504 | |a Includes bibliographical references (pages 205-211) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |6 880-01 |t Volume preserving homeomorphisms of the cube -- |t Introduction to part I and II (compact manifolds) -- |t Measure preserving homeomorphisms -- |t Discrete approximations -- |t Transitive homeomorphisms of In and Rn -- |t Fixed points and area preservation -- |t Measure preserving lusin theorem -- |t Ergodic homeomorphisms -- |t Uniform approximation in g[In, delta] and generic properties in M[In, delta] -- |t Measure preserving homeomorphisms of a compact manifold -- |t Measures on compact manifolds -- |t Dynamics on compact manifolds -- |t Oeasure preserving homeomorphisms of a noncompact manifold -- |t Ergodic volume preserving homeomorphisms of Rn -- |t Manifolds where ergodicity is not generic -- |t Noncompact manifolds and ends -- |t Ergodic homeomorphisms: the results -- |t Ergodic homeomorphisms: proofs -- |t Other properties typical in M[X, u]. |
| 520 | |a This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley-Zehnder- Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Homeomorphisms. | |
| 650 | 0 | |a Measure-preserving transformations. | |
| 650 | 6 | |a Homéomorphismes. | |
| 650 | 6 | |a Transformations conservant la mesure. | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Homeomorphisms |2 fast | |
| 650 | 7 | |a Measure-preserving transformations |2 fast | |
| 650 | 7 | |a Homöomorphismengruppe |2 gnd | |
| 650 | 7 | |a Ergodentheorie |2 gnd | |
| 650 | 7 | |a Dynamisches System |2 gnd | |
| 650 | 7 | |a Sistemas dinâmicos. |2 larpcal | |
| 650 | 7 | |a Dinâmica topológica. |2 larpcal | |
| 650 | 7 | |a Homéomorphismes. |2 ram | |
| 650 | 7 | |a Transformations (mathématiques) |2 ram | |
| 700 | 1 | |a Prasad, V. S., |d 1950- | |
| 776 | 0 | 8 | |i Print version: |a Alpern, Steve, 1948- |t Typical dynamics of volume preserving homeomorphisms. |d Cambridge ; New York : Cambridge University Press, 2000 |z 0521582873 |w (DLC) 00031258 |w (OCoLC)44083978 |
| 830 | 0 | |a Cambridge tracts in mathematics ; |v 139. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=112402 |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g pt. I |t Volume Preserving Homeomorphisms of the Cube -- |g 1. |t Introduction to Parts I and II (Compact Manifolds) -- |g 1.1. |t Dynamics on Compact Manifolds -- |g 1.2. |t Automorphisms of a Measure Space -- |g 1.3. |t Main Results for Compact Manifolds -- |g 2. |t Measure Preserving Homeomorphisms -- |g 2.1. |t Spaces M, H, G -- |g 2.2. |t Extending a Finite Map -- |g 3. |t Discrete Approximations -- |g 3.1. |t Introduction -- |g 3.2. |t Dyadic Permutations -- |g 3.3. |t Cyclic Dyadic Permutations -- |g 3.4. |t Rotationless Dyadic Permutations -- |g 4. |t Transitive Homeomorphisms of In and Rn -- |g 4.1. |t Transitive Homeomorphisms -- |g 4.2. |t Transitive Homeomorphism of In -- |g 4.3. |t Transitive Homeomorphism of Rn -- |g 4.4. |t Topological Weak Mixing -- |g 4.5. |t Chaotic Homeomorphism of In -- |g 4.6. |t Periodic Approximations -- |g 5. |t Fixed Points and Area Preservation -- |g 5.1. |t Introduction -- |g 5.2. |t Plane Translation Theorem -- |g 5.3. |t Open Square -- |g 5.4. |t Torus -- |g 5.5. |t Annulus -- |g 6. |t Measure Preserving Lusin Theorem -- |g 6.1. |t Introduction -- |g 6.2. |t Approximation Techniques -- |g 6.3. |t Proof of Theorem 6.2(i) -- |g 7. |t Ergodic Homeomorphisms -- |g 7.1. |t Introduction -- |g 7.2. |t Classical Proof of Generic Ergodicity -- |g 8. |t Uniform Approximation in G[In, λ] and Generic Properties in M[In, λ] -- |g 8.1. |t Introduction -- |g 8.2. |t Rokhlin Towers and Stochastic Matrices -- |g pt. II |t Measure Preserving Homeomorphisms of a Compact Manifold -- |g 9. |t Measures on Compact Manifolds -- |g 9.1. |t Introduction to Part II -- |g 9.2. |t General Measures on the Cube -- |g 9.3. |t Manifolds -- |g 9.4. |t Measures on Compact Manifolds -- |g 9.5. |t Typical Properties in M[X, μ] -- |g 10. |t Dynamics on Compact Manifolds -- |g 10.1. |t Introduction -- |g 10.2. |t Genericity Results for Manifolds -- |g 10.3. |t Applications to Fixed Point Theory -- |g pt. III |t Measure Preserving Homeomorphisms of a Noncompact Manifold -- |g 11. |t Introduction to Part III -- |g 11.1. |t Noncompact Manifolds -- |g 11.2. |t Topologies on G[X, μ] and M[X, μ]: Noncompact Case -- |g 11.3. |t Main Results for Sigma Compact Manifolds -- |g 11.4. |t Outline of Part III -- |g 12. |t Ergodic Volume Preserving Homeomorphisms of Rn -- |g 12.1. |t Introduction -- |g 12.2. |t Homeomorphisms of Rn with Invariant Cubes -- |g 12.3. |t Generic Ergodicity in M[Rn, λ] -- |g 12.4. |t Other Typical Properties in M[Rn, λ] -- |g 13. |t Manifolds Where Ergodicity Is Not Generic -- |g 13.1. |t Introduction -- |g 13.2. |t Two Examples -- |g 13.3. |t Ends of a Manifold: Informal Introduction -- |g 13.4. |t Another Look at Rn -- |g 13.5. |t Flip on the Strip -- |g 13.6. |t Flip on Manhattan -- |g 13.7. |t Shear Map on the Strip -- |g 14. |t Noncompact Manifolds and Ends -- |g 14.1. |t Introduction -- |g 14.2. |t End Compactification -- |g 14.3. |t Examples of End Compactifications -- |g 14.4. |t Algebra Q of Clopen Sets -- |g 14.5. |t Measures on Ends -- |g 14.6. |t Compact Separating Sets -- |g 14.7. |t End Preserving Lusin Theorem -- |g 14.8. |t Induced Homeomorphism h -- |g 14.9. |t Charge Induced by a Homeomorphism -- |g 14.10. |t h-moving Separating Sets -- |g 14.11. |t End Conditions for Homeomorphic Measures -- |g 15. |t Ergodic Homeomorphisms: The Results -- |g 15.1. |t Introduction -- |g 15.2. |t Consequences of Theorem 15.1 -- |g 16. |t Ergodic Homeomorphisms: Proofs -- |g 16.1. |t Introduction -- |g 16.2. |t Outline of Proofs of Theorems 15.1 and 15.2 -- |g 16.3. |t Proof of Theorem 15.1: Strip Manifold -- |g 16.4. |t Proofs of Theorems 15.1 and 15.2: General Case -- |g 17. |t Other Properties Typical in M[X, μ] -- |g 17.1. |t General Existence Result -- |g 17.2. |t Proof of Theorem 17.1 -- |g 17.3. |t Weak Mixing End Homeomorphisms -- |g 17.4. |t Maximal Chaos on Noncompact Manifolds -- |g Appendix 1 |t Multiple Rokhlin Towers and Conjugacy Approximation -- |g A1.1. |t Introduction -- |g A1.2. |t Skyscraper Constructions -- |g A1.3. |t Multiple Tower Rokhlin Theorem -- |g A1.4. |t Pointwise Conjugacy Approximation -- |g A1.5. |t Specified Transition Probabilities -- |g A1.6. |t Setwise Conjugacy Approximation -- |g A1.7. |t Infinite Measure Constructions -- |g Appendix 2 |t Homeomorphic Measures -- |g A2.1. |t Introduction -- |g A2.2. |t Homeomorphic Measures on the Cube -- |g A2.3. |t Homeomorphic Measures on Compact Manifolds -- |g A2.4. |t Homeomorphic Measures on Noncompact Manifolds -- |g A2.5. |t Proof of the Berlanga--Epstein Theorem. |
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